Typically, when a uniaxial load is applied to a spring, the spring exhibits a linear compression rate. That is to say, it takes twice as much force to compress a typical spring two inches as it does to compress the same spring one inch. The linear response of springs is expressed by Hooke's law which states that the force (F) needed to extend or compress a spring by some distance (D) is proportional to that distance. This relationship is expressed mathematically as F=kD, where k represents the spring constant for a particular spring. A high spring constant indicates that the spring requires more force to compress, and a low spring constant means the spring requires less force to compress.
Linear response springs, such as wire coil springs, are commonly used as mattress innersprings in combination with padding and upholstery that surround the innersprings. Most mattress innersprings are comprised of an array of wire coil springs which are often adjoined by lacing end convolutions of the coil springs together with cross wires. An advantage of this arrangement is that it is inexpensive to manufacture. However, this type of innerspring often provides a firm and rigid mattress surface.
An alternative to an innerspring mattress is a mattress constructed of one or more foam layers. Unlike an innerspring mattress comprised of an array of wire coil springs, foam mattresses exhibit a non-linear response to forces applied to the mattress. In particular, a foam mattress provides more support as the load increases. For instance, a typical foam mattress provides increased support after it has been compressed approximately 60% of the maximum compression of the foam. The non-linear response of foam mattresses provides improved sleep comfort for a user. However, the mechanical properties of certain foam may degrade over time affecting the overall comfort of the foam mattress. Furthermore, foam mattresses are often more costly to produce than metal spring mattresses.